That's actually a modern invention. Originally, 他 (they, sg.) was the only one used, but then someone added 她 for the literal sole purpose of translating western European works -- as in many of those languages there, it's all gendered.

Try to translate this for example:
"He wants a cookie, and she wants a mango."

If translated literally-ish, you'd write:
他有饼干和他有芒果, which yields "They want a cookie, and they want a mango". It's ambiguous.

So if one really wanted that, why (in my view) not do it as: "他有饼干和那女的有芒果"? That meaning, "They want a cookie, and that gal wants a mango." And then later when referring to only the gal in an unambiguous context, just use 他 anyways.

I feel like it'd be funnier if 男 ”man" was incorporated into the original pronoun, then you could have 也 with either 亻(that then yields 他), or with 男 (男也) or with 女 (她). And then you only use the male and female ones if you explicitly want to be so annoyingly gendery.

Then we can use the neutral pronoun for all purposes. Or, y'know, just use the neutral pronoun as originally done. Which still can be done, it's just dated.